The Boundary Element Method (BEM) is a very efficient numerical method to simulate wave propagation in large-scale (unbounded) domains. But the fully-populated nature of the system matrix drastically reduces its practical uses. For this reason, a lot of work in the community has been devoted to the derivation of fast techniques to perform the matrix vector product needed in the iterative solver, making now one iteration very cheap. However, it has been shown that the new issue with BEMs is the number of iterations. It can significantly hinder the overall efficiency of fast BEMs. The derivation of robust preconditioners is now inevitable to increase the size of the problems that can be considered. I will explain why such a derivation is difficult in the context of fast BEMs and present some recent works on the derivation of algebraic preconditioners for fast BEMs. I will also present a companion tool to reduce the computational cost: mesh adaptation techniques for fast BEMs. I will show a lot of applications where these methods are interesting and can model real physical problems. Speaker(s): Stéphanie Chaillat (ENSTA-Paris)